Calculating Size of Star Image with Converging Lens

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In summary, when using a converging lens with a diameter of 50mm and a focal length of 500mm to produce an image of a point source (star) at infinity, the resulting image will have a diameter of approximately 8mm, calculated using diffraction principles. However, because of the distances involved, the star can be regarded as a point source from an optical standpoint. The size of the resulting image is also dependent on the star's relative magnitude and the optics of the imaging system. While planets in the Solar System may have a distinguishable angular diameter, stars are essentially point sources.
  • #1
Emilyjoint
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An image of a point source (star) at infinity produces an image using a converging lens of diameter 50mm and focal length 500mm. Calculate the diameter of the resulting image.(take wavelengthof light to be 4x10^-7m)
I ask this because it is to do with seeing stars through a telescope.
I think the diameter is caclulated using diffraction principles to be 8mm Can anyone check to see if you get the same answer.
I used Sinθ = λ/a
 
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  • #2
A star is not a point source.

A star is a ball.
 
  • #3
Char. Limit said:
A star is not a point source.

A star is a ball.

That is essentially true, but because of the distances involved it can be regarded as a point source from an optical point of view

Dave
 
  • #4
OK./...would a point source produce an image of this size?
 
  • #6
Looked at that but could not see how it relates to a point source.
S it OK to use Sin theta = λ/a to calculate th width
 
  • #8
Thanks for the help.Used the Calc site and got 9x10^-3mm...i had made a mistake with units.
got it now
 
  • #9
Emilyjoint said:
OK./...would a point source produce an image of this size?

The size of image from a star is dependent on its relative magnitude (brightness) and the optics of your imaging system (diffraction and other aberrations). There is no clue about the angle subtended by it at the Earth.

(Most) planets in the Solar System subtend a big enough angle to distinguish the actual angular diameter of their disc (they look like little moons) but even the nearest star is a 'point' source to all intents and purposes.
 

FAQ: Calculating Size of Star Image with Converging Lens

1. How do I calculate the size of a star image using a converging lens?

The size of a star image can be calculated by using the formula S = (D/f) * s, where S is the size of the star image, D is the distance between the lens and the star, f is the focal length of the lens, and s is the size of the star.

2. What is the focal length of a converging lens?

The focal length of a converging lens is the distance between the center of the lens and the point where the light rays converge. It is typically measured in millimeters (mm) or centimeters (cm).

3. How do I measure the distance between the lens and the star?

The distance between the lens and the star can be measured using a ruler or a measuring tape. Make sure to measure from the center of the lens to the center of the star.

4. Can I use this formula to calculate the size of any object?

Yes, this formula can be used to calculate the size of any object as long as the object is far enough away from the lens and the lens is of a known focal length.

5. What is the unit of measurement for the size of the star image?

The unit of measurement for the size of the star image will depend on the units used for distance (D) and focal length (f). For example, if D and f are measured in centimeters, the size of the star image (S) will also be in centimeters.

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